Section 9.2 Sampling Proportions

1. Section 9.2Sampling Proportions AP Statistics

2. Example • A Gallup Poll found that 210 out of a random sample of 501 American teens age 13 to 17 knew the answer to this question: • “What year did Columbus ‘discover’ America?” AP Statistics, Section 9.2

3. Interpretation • 210/501 =.42 • Is .42 a parameter or a statistic? • Does this mean that only 42% of American teens know this fact? • What is the proper notation for this statistic? • p-hat = .42 AP Statistics, Section 9.2

4. New Formulas AP Statistics, Section 9.2

5. Rules of Thumb • Use the previous formula for standard deviation only when the population is at least 10 times as large as the sample. • You may use the normal approximation to the sampling distribution of p-hat for the values n and p that satisfy np>10 and nq>10 AP Statistics, Section 9.2

6. Do we meet the rules of thumb • Do we believe the population is bigger than 10*501? • Do we believe np>10 and nq>10? AP Statistics, Section 9.2

7. Draw the distribution… AP Statistics, Section 9.2

8. Different question • An SRS of 1500 first-year college students were asked whether they applied for admission to any other college. In fact, 35% of all first-year students applied to colleges beside the one they are attending. • What is the probability that the poll will be within 2 percentage points of the true p? AP Statistics, Section 9.2

9. AP Statistics, Section 9.2

10. Conclusion • About 90% of the samples fall within 2% of the real p. AP Statistics, Section 9.2

11. Another example • One way of checking the effect of undercoverage, nonresponse, and other sources of error in a sample survey is to compare the sample with known facts about the population. • About 11% of American adults are black. The proportion p-hat in an SRS should be about .11. • If a national sample contains only 9.2% blacks, should we suspect nonresponse bias? AP Statistics, Section 9.2

12. AP Statistics, Section 9.2

13. Exercises • 9.19-9.29 odd AP Statistics, Section 9.2